There are a variety of applications where it is desirable to use a positioning system to determine the two-dimensional (2D) or three-dimensional (3D) position of a target object, such as manufacturing, assembly, construction, etc. A positioning system may use an array of sensors that measure or determine a distance to the target object. The positioning system then calculates the position (e.g., x,y or x,y,z) of the target object in a coordinate system based on the positions of the sensors, and the distance from the sensors to the target object.
Before a positioning system is used for measurements, the system is typically calibrated to determine the position (e.g., x,y,z) of the sensors in the array. Before calibration, the positions of the sensors are estimated using a tape measure, a laser measuring device, etc. After the sensor positions are estimated, an operator attempts to calibrate the sensor positions with hardware in the loop. This normally entails precisely surveying one or more target objects in the field of the sensor array. Each sensor then measures a distance to the target objects as a comparison to see how close the measurements are to the true surveyed distances. Adjustments may then be made to the estimated positions of the sensors using least squares, simplex, optimization algorithms, regression models, etc., to determine calibrated sensor positions. After calibration, the positioning system uses the calibrated sensor positions to determine the position of a target object in a coordinate system. If the calibrated sensor positions are not accurately determined during calibration, the measurements of the positioning system will likewise not be accurate.
Even though the calibrated sensor positions may be mathematically correct, it is difficult to determine if the calibrated sensor positions are actually correct so that a true position of the target object is provided. It would be desirable to verify that the calibrated sensor positions being used in the calculations are accurate.